# Best Arm Identification for Cascading Bandits in the Fixed Confidence Setting

@inproceedings{Zhong2020BestAI, title={Best Arm Identification for Cascading Bandits in the Fixed Confidence Setting}, author={Zixin Zhong and Wang Chi Cheung and Vincent Yan Fu Tan}, booktitle={International Conference on Machine Learning}, year={2020} }

We design and analyze CascadeBAI, an algorithm for finding the best set of $K$ items, also called an arm, within the framework of cascading bandits. An upper bound on the time complexity of CascadeBAI is derived by overcoming a crucial analytical challenge, namely, that of probabilistically estimating the amount of available feedback at each step. To do so, we define a new class of random variables (r.v.'s) which we term as left-sided sub-Gaussian r.v.'s; these are r.v.'s whose cumulant…

## 6 Citations

### Best Arm Identification in Restless Markov Multi-Armed Bandits

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A sequential policy that forcibly selects an arm that has not been selected for R consecutive time instants is proposed, and it is shown that this policy achieves an upper bound that depends on R and is monotonically non-increasing as R → ∞ .

### Optimal Clustering with Bandit Feedback

- Materials ScienceArXiv
- 2022

Junwen Yang Institute of Operations Research and Analytics, National University of Singapore, Singapore 117602, junwen yang@u.nus.edu Zixin Zhong Department of Electrical and Computer Engineering,…

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Frank-Wolfe-based Sampling (FWS) is devised, a simple algorithm whose sample complexity matches the lower bounds for a wide class of pure exploration problems and is competitive compared to state-of-art algorithms.

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The first polynomial-time adaptive algorithm is designed, which simultaneously addresses limited feedback, general reward function and combinatorial action space (e.g., matroids, matchings and s-t paths), and provides its sample complexity analysis.

### Probabilistic Sequential Shrinking: A Best Arm Identification Algorithm for Stochastic Bandits with Corruptions

- Computer ScienceICML
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A novel randomized algorithm, Probabilistic Sequential Shrinking (PSS), which is agnostic to the amount of corruptions, and has a better performance than its deterministic analogue, the Successive Halving algorithm by Karnin et al. (2013).

### Combinatorial Pure Exploration with Full-bandit Feedback and Beyond: Solving Combinatorial Optimization under Uncertainty with Limited Observation

- Computer ScienceArXiv
- 2020

Recently proposed techniques for combinatorial pure exploration problems with limited feedback for multi-armed bandits with semi-bandit feedback are reviewed.

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